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Laser diode response to deep sinusoidal injection current modulation is investigated both theoretically and experimentally. By the numerical analysis of multilongitudinal rate equations with a modulation term, regular pulsation regions and the spectral broadening and wavelength shift of the optical pulse are given. These theoretical results are well supported by experimental observations with an AlGaAs laser diode, where a 40-70 ps optical pulse at a repetition rate of 200 MHz to 2.17 GHz was obtained. The possibility of generating a coherent optical pulse by harmonic frequency injection current modulation of laser diodes without external cavities is pointed out theoretically. Further, coherent pulsations by external light injection in sinusoidally modulated laser diodes are investigated both theoretically and experimentally.